#Question 1
using JuMP, Cbc

m=Model()
@variable(m, x1 >= 0)
@variable(m, x2 >= 0)
@variable(m, x3 >= 0)

@objective(m, Max, -x1+2x2+0.5x3)

@constraint(m, constraint1, 2x1-x2 >= 1)
@constraint(m, constraint2, 2x1+3x3 <= 3)

set_optimizer(m, Cbc.Optimizer)
optimize!(m)

#display the solution
println("optimal value of x1: ", value(x1))
println("optimal value of x2: ", value(x2))
println("optimal value of x3: ", value(x3))
println("optimal objective: ", objective_value(m))

optimal value of x1: 1.5
optimal value of x2: 2.0
optimal value of x3: 0.0
optimal objective: 2.5
Presolve 0 (-2) rows, 0 (-3) columns and 0 (-4) elements
Optimal - objective value 2.5
After Postsolve, objective 2.5, infeasibilities - dual 0 (0), primal 0 (0)
Optimal objective 2.5 - 0 iterations time 0.002, Presolve 0.00

Question 2-1 Maximum (5x1+4x2) becomes optimal at x1 = 3 and x2 = 1.5

Question 2-2 Maximum (10x2) becomes optimal at x2 = 2

#Question 3


Maximize
30x1+60x2+50x3 #Maximize Money

subject to (Constraints)
x1, x2, x3 >= 0
40x1 + 20x2 + 30x3 <= 900 #Tulips
15x1 + 25x2 + 30x3 <= 700 #Daffodils
10x1 + 15x2 + 20x3 <= 500 #Hyacinths

UndefVarError: `Maximize` not defined

#Question 4-1

Minimize
8x1 + 4x2 #We want to minimize cost

Subject to (Constraints)
5x1+15x2 >= 50 #Carbohydrates
50x1 + 5x2 >= 40 #Protein
15x1 + 2x2 >= 60 #Fat
x1 >= 0
x2 >= 0

UndefVarError: `Minimize` not defined

QUESTION 4-2) Professor Smith's Friend gets to eat 0.8 steaks, and 0 french fries

Question 5-1) This LP becomes optimal when x1 = 0,10 & x2 = -1,1

Question 5-2) This LP has infinite solutions. Due to it's constraints, it has an infinite amount of solutions.

Question 5-3 Part A) LP becomes optimal @ x1 = 10 and x2 = 1

Question 5-3 Part B) Unique Optimal Solution same as part A

#Question 5-4
Answer = "We call this Linear Program with this objective UNBOUNDED, as the LP can reach INFINITY"
Answer

"We call this Linear Program with this objective constraints UNBOUNDED, as the LP can reach INFINITY"